Explicit Predictor–multicorrector Time Discontinuous Galerkin Methods for Linear Dynamics

Abstract

This paper focuses on the formulation and implementation of explicit predictor} multicorrector Time Discontinuous Galerkin methods for linear structural dynamics. The formulation of the schemes is based on piecewise linear functions in time that approximate displacements and momenta. Both the predictors and correctors are designed to inherit third order accuracy from the exact parent implicit Time Discontinuous Galerkin method. Moreover, they are endowed with large stability limits and controllable numerical dissipation by means of an algorithmic parameter. Thereby, the resulting algorithms appear to be competitive with standard explicit algorithms for structural dynamics. Representative numerical simulations are presented illustrating the performance of the proposed numerical schemes and con"rming the analytical results.

Explicit Predictor–multicorrector Time Discontinuous Galerkin Methods for Non-Linear Dynamics

“…The formulation represents an extension to the non-linear case of the explicit methods suggested in reference [17]. Therefore, an accuracy and stability analysis of these schemes is needed for the non-linear case.…”

“…Based on similar strategies, a new class of explicit TDG methods, with a user-de"ned dissipation, has been developed by Bonelli et al [17]. The new proposed schemes, designated E schemes, have been implemented in a predictor}multicorrector form, exhibit third order accuracy and accrue a stability limit higher than the one of the CD scheme.…”

Vibration analysis for elastic multi‐beam structures by the C0‐continuous time‐stepping finite element method

“…On the other hand, owing to (27), Collecting the last two equations, we can write the LHS of (36) as…”

“…However, there is some disadvantage for such type of methods, since a (4×4) block system must be solved at each time step, which is two times as large as that discretized in view of the primal variable. To remedy this difficulty, many efficient iterative algorithms [27][28][29][30][31][32] were developed for the TDG method. It is noted that the methods in [20,21,26] have also been extended to discuss dynamic phase transition problems in linear elastic media [33,34].…”

Analysis and performance of a predictor‐multicorrector Time Discontinuous Galerkin method in non‐linear elastodynamics

“…As a consequence, there is an interest in reducing the computational expense without degrading the accuracy and stability properties. Predictor-multicorrector solution procedures are an attractive approach towards this objective and some competitive algorithms of this type have been developed for linear systems [14][15][16]. More speciÿcally, Li and Wiberg [15] implemented a predictormulticorrector solution algorithm in the TDG method.…”